Question 771173
Just use meaning of perimeter, like r for rows, c for columns.  Perimeter of 24 would be 2*r+2*c, and then you want all integer (really, natural numbers) values for r and c for which 2r+2c=24.  You can use the simpler equation, r+c=12.  

The question then becomes, which combinations of whole numbers will give you the sum of 12?